Solving Pell's equation using suborbital graphs

被引：0

作者：

Koroglu, Tuncay ^{[1
]}

机构：

[1] Karadeniz Tech Univ, Trabzon, Turkiye

来源：

FILOMAT | 2024年 / 38卷 / 19期

关键词：

Modular group action; Suborbital graph; Pell's equation; CONGRUENCE SUBGROUPS;

D O I：

10.2298/FIL2419863K

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish a connection between suborbital graphs and integer solutions of Pell's equation of the form x(2) - Ny(2) = 1, where N is a non-square positive integer. We derive new suborbital graphs generated by the action of some specific modular subgroups on extended rational numbers. By using these graphs, we obtain a new combinatorial notation for the integer solutions of Pell's equation and some results on the vertices of the graphs studied here.

引用

页码：6863 / 6870

页数：8

共 36 条

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